Asymptotic and Analytic Methods in Stochastic Evolutionary Symptoms

• Record Nr.: UNINA9911020152403321
• Autore: Koroliouk Dmitri
• Pubbl/distr/stampa: Newark : , : John Wiley & Sons, Incorporated, , 2023; ©2023
• ISBN: 9781394229482; 1394229488; 9781394229468; 1394229461
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (261 pages)
• Altri autori (Persone): SamoilenkoIgor
• Disciplina: 530.155353
• Soggetti: Stochastic processes; Diffusion processes
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Introduction -- Chapter 1. Multidimensional Models of Kac Type -- 1.1.Definitions and basic properties -- 1.2.Moments of evolutionary process -- 1.3. Systems of Kolmogorov equations -- 1.4. Evolutionary operator and theorem about weak convergence to themeasure of theWiener process -- Chapter 2. Symmetry of Markov Random Evolutionary Processes in Rn -- 2.1. Symmetrization: definition and properties -- 2.2. Examples of symmetric distributions in Rn and distributions on n + 1-hedra -- 2.2.1. Symmetricdistributions -- 2.2.2. Distributions on n + 1-hedra -- Chapter 3. Hyperparabolic Equations, Integral Equation and Distribution for Markov Random Evolutionary Processes -- 3.1. Hyperparabolic equations and methods of solving Cauchy problems -- 3.2. Analytical solution of a hyperparabolic equation with real-analytic initial conditions -- 3.3. Integral representation of the hyperparabolic equation -- 3.4.Distributionfunction of evolutionary process -- Chapter 4. Fading Markov Random Evolutionary Process -- 4.1. Definition of fading Markov random evolutionary process, its moments and limit distribution -- 4.2. Integral equation for a function from the fading ; random evolutionary process -- 4.3. Equations in partial derivatives for a function of the fading random evolutionary process -- Chapter 5. Two Models of the Evolutionary Process -- 5.1.Evolution on a complex plane -- 5.2.Evolutionwithinfinitelymany directions -- 5.2.1. Symmetric case -- 5.2.2.Non-symmetric case -- Chapter 6. Diffusion Process with Evolution and Its Parameter Estimation -- 6.1.Asymptotic diffusion environment -- 6.2. Approximation of a discrete Markov process in asymptotic diffusion environment -- 6.3. Parameter estimation of the limit process -- Chapter 7. Filtration of Stationary Gaussian Statistical Experiments.; 7.1. Introduction -- 7.2. Stochastic difference equation of the process of filtration -- 7.3.Coefficient of filtration -- 7.4.Equation of optimal filtration -- 7.5.Characterization of afilteredsignal -- Chapter 8. Adapted Statistical Experiments with Random Change of Time -- 8.1. Introduction -- 8.2. Statistical experiments and evolutionary processes -- 8.3. Stochastic dynamics of statistical experiments -- 8.4.Adapted statistical experiments in series scheme -- 8.5.Convergence of the adapted statistical experiments -- 8.6. Scaling parameter estimation -- 8.7. Statistical estimations of the renewal intensity parameter -- 8.7.1. Poisson's renewal process with parameter q = 2 -- 8.7.2. Stationary renewal process with delay, determined by the initial distribution function of the limit overjumps -- 8.7.3.Renewal processeswith arbitrarilydistributed renewal intervals -- Chapter 9. Filtering of Stationary Gaussian Statistical Experiments -- 9.1. Stationary statistical experiments -- 9.2. Filtering of discrete Markov diffusion -- 9.3.Thefilteringerror -- 9.4.Thefilteringempirical estimation -- Chapter 10. Asymptotic Large Deviations for Markov Random Evolutionary Process -- 10.1.Asymptotic largedeviations -- 10.2. Asymptotically stopped Markov random evolutionary process -- 10.3.Explicit representation for the normalizing function -- Chapter 11. Asymptotic Large Deviations for Semi-Markov Random Evolutionary Processes -- 11.1. Recurrent semi-Markov random evolutionary processes -- 11.2.Asymptotic largedeviations -- Chapter 12. Heuristic Principles of Phase Merging in Reliability Analysis -- 12.1.The duplicated renewal system -- 12.2.The duplicated renewal systemin the series scheme -- 12.3.Heuristic principles of the phasemerging -- 12.4. The duplicated renewal system without failure -- References -- Index -- EULA.
• Sommario/riassunto: This book, 'Asymptotic and Analytic Methods in Stochastic Evolutionary Systems', authored by Dmitri Koroliouk and Igor Samoilenko, offers an in-depth analysis of stochastic evolutionary processes using asymptotic and analytic methods. It explores various models and equations such as those of the Kac type, symmetry in Markov random processes, and fading Markov processes. The text includes discussions on integral equations, diffusion processes, and statistical experiments with random changes in time. Aimed at researchers and scholars in the fields of mathematics and statistics, the book serves as a comprehensive guide for understanding complex stochastic systems, providing both theoretical foundations and practical applications.